Timeline for Kac Moody algebra defintion
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 27, 2014 at 20:50 | vote | accept | Sven Cattell | ||
| Jan 11, 2014 at 2:38 | answer | added | S. Carnahan♦ | timeline score: 4 | |
| Sep 6, 2013 at 14:04 | comment | added | Sven Cattell | I think you have a good answer to my admittingly soft question. | |
| Sep 5, 2013 at 21:47 | comment | added | S. Carnahan♦ | One reason why the extra dimensions are useful is that you end up with a nondegenerate inner product on the weight space. In your first example, your weight space becomes a singular plane embedded in $\mathbb{R}^{2,1}$, and it's harder to see the geometry attached to reflections. | |
| Sep 5, 2013 at 21:44 | comment | added | Sven Cattell | I find this dimension in every definition I have read. The Serre relations are all implemented slightly differently, but the dimension of the Cartan subalgebra is always $n+\text{corank}(A)$. | |
| Sep 5, 2013 at 21:41 | history | edited | Sven Cattell | CC BY-SA 3.0 |
added 103 characters in body
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| Sep 5, 2013 at 21:22 | history | edited | Jim Humphreys |
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| Sep 5, 2013 at 21:21 | comment | added | Jim Humphreys | Probably part of the problem is that "the" definition doesn't really exist, just a range of closely related definitions. The ideas come from the independent thesis work of Kac and of Moody, but later developments tweaked the notions in various ways. It's a good idea to say more explicitly what version you are looking at. | |
| Sep 5, 2013 at 19:37 | history | asked | Sven Cattell | CC BY-SA 3.0 |